Abstract This paper proposes a novel algorithm for manifold alignment preserving global geometry. This approach constructs mapping functions that project data instances from different input domains to a new lower-dimensional space, simultaneously matching the instances in correspondence and preserving global distances between instances within the original domains. In contrast to previous approaches, which are largely based on preserving local geometry, the proposed approach is suited to applications where the global manifold geometry needs to be respected. We evaluate the effectiveness of our algorithm for transfer learning in two real-world cross-lingual information retrieval tasks.